Beek and Tuck 
where P(x) is the amplitude of the pressure in a unit amplitude in- 
cident wave i.e. 
ikx cosB 
e 
P(x) = pg (AIII. 3) 
Equation (AIII.3) neglects pressure variations with y and z over 
the '"'end plates'' , consistent with the slender body assumption. 
Thus 
= -2ipg S sin(k 1 cosB ) (AIII, 4) 
F. 
10 0 
On the other hand, the original formula (3.1) leads to the 
ridiculous result T,, = 0, since S'(x)=0 for |x|<! with this 
ship. This is reflected in the modified formula (AIII.1) by the fact 
that the integrated part cancels the integral exactly. In fact if we 
"neglect'' the integral part in (AIII.1) , leading to 
e 
T = - pgik cose | de Sere are, (ATI. 5) 
10 
at 
we obtain the correct result (AIII.4) for the special case S(x) = Sg = 
constant ! 
Thus it would seem that the correct procedure is to disregard 
integrated parts on integrating S'(x) by parts. This is equivalent to 
saying that all ships actually have zero area at their ends, so thata 
transom is replaced by a very rapid decrease to zero area, If the 
ship in fact has no transom this question does not arise, of course, 
and the only example used in the present paper comes into this cate- 
gory. 
Although the justification is far from obvious, we have used 
the same procedure in all integrals involving S'(x) . For instance, 
the Fourier transform A‘ required in (AII.1) is actually evaluated 
as 
Ay (Ky = a dx S(x) gee 3 (AIII, 6) 
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